The Cosmic Linear Anisotropy Solving System (CLASS) IV: Efficient implementation of non-cold relics

Abstract: We present a new flexible, fast and accurate way to implement massive neutrinos, warm dark matter and any other non-cold dark matter relics in Boltzmann codes. For whatever analytical or numerical form of the phase-space distribution function, the optimal sampling in momentum space compatible with a given level of accuracy is automatically found by comparing quadrature methods. The perturbation integration is made even faster by switching to an approximate viscous fluid description inside the Hubble radius, which differs from previous approximations discussed in the literature. When adding one massive neutrino to the minimal cosmological model, CLASS becomes just 1.5 times slower, instead of about 5 times in other codes (for fixed accuracy requirements). We illustrate the flexibility of our approach by considering a few examples of standard or non-standard neutrinos, as well as warm dark matter models.

• The paper presents a novel momentum sampling scheme that minimizes computational overhead while ensuring simulation accuracy.
• It introduces a fast perturbation integration method using a viscous fluid approximation to significantly reduce computation time.
• The work supports arbitrary phase-space distributions for non-cold dark matter, enhancing flexibility in modeling various cosmological scenarios.

Overview of the Cosmic Linear Anisotropy Solving System (CLASS) for Non-Cold Relics

The paper presents a sophisticated extension of the Cosmic Linear Anisotropy Solving System (CLASS) that enhances the computational efficiency and flexibility of simulating non-cold relics in cosmology. Non-cold relics include massive neutrinos and warm dark matter (WDM), which are crucial for understanding the universe's evolution at various scales. The approach in this research is both innovative and pragmatic, paving the way for accurate cosmological simulations that account for these components' unique behaviors without sacrificing computational efficiency.

Key Contributions

1. Momentum Space Sampling: The paper introduces an automatic quadrature comparison scheme to determine optimal momentum sampling in Boltzmann codes. This ensures that the momentum grid is efficiently utilized, minimizing computational overhead while maintaining desired accuracy levels.
2. Fast Perturbation Integration: A novel approximation is presented, which switches to a viscous fluid description within the Hubble radius. This reduces computational time compared with existing models by a factor of 3 when one massive neutrino is included in the minimal cosmological model.
3. Implementation of NCDM Species: CLASS now supports arbitrary forms of phase-space distribution functions for non-cold dark matter (NCDM) species. This flexibility allows researchers to simulate a wide array of cosmological scenarios, from standard massive neutrinos to various warm dark matter models, as demonstrated through several examples.

Numerical Performance

The improvements to CLASS significantly boost performance. The execution time scales more favorably as the number of perturbed variables is reduced—enhanced by reducing momentum and switching to a fluid approximation where suitable. This optimization shows a remarkable improvement, making CLASS approximately 1.5 times slower for one massive neutrino, a notable reduction from being 5 times slower, which is typical in similar Boltzmann codes.

Theoretical and Practical Implications

The adaptability of the CLASS code ensures that it can seamlessly incorporate different theoretical models of neutrinos and dark matter, which differ from the standard thermal relics. This paves the way for new investigations into the implications of non-standard neutrino interactions and the exploration of dark matter properties. With CLASS, researchers can simulate various models with non-thermal corrections or investigate resonance-produced species, thereby expanding our understanding of particle physics within a cosmological context.

Future Developments

Future extensions of the CLASS code could further refine the approximations introduced, especially for high-precision demands on sub-Hubble dynamic regimes. Additionally, integration of CLASS with other data-driven models, such as those influenced by observational cosmology, might allow for more expansive exploration of parameter spaces in cosmological studies.

The advancements encapsulated in this paper exemplify a strategic balance between computational efficiency and model flexibility, enabling exploration of complex cosmological phenomena. This contributes to the ongoing refinement of our cosmological models and understanding of the universe, reiterating the necessity of robust tools in theoretical cosmology. The methodologies detailed here could inspire similar approaches in the simulation of other complex astrophysical and particle physics systems.